U.S. patent number 4,789,117 [Application Number 06/947,164] was granted by the patent office on 1988-12-06 for bodies with reduced base drag.
This patent grant is currently assigned to United Technologies Corporation. Invention is credited to Robert W. Paterson, Walter M. Presz, Jr., Michael J. Werle.
United States Patent |
4,789,117 |
Paterson , et al. |
December 6, 1988 |
Bodies with reduced base drag
Abstract
A body adapted to move downstream through a fluid has a
downstream extending smooth surface terminating at a blunt base. A
plurality of adjacent U-shaped, downstream extending troughs in the
smooth surface intersect the blunt base to form trough outlets. The
troughs are appropriately spaced apart, sized and configured to
flow full over their entire length and cause fluid to flow into the
space immediately behind the blunt base, thereby reducing base drag
on the body.
Inventors: |
Paterson; Robert W. (Simsbury,
CT), Werle; Michael J. (West Hartford, CT), Presz, Jr.;
Walter M. (Wilbraham, MA) |
Assignee: |
United Technologies Corporation
(Hartford, CT)
|
Family
ID: |
25485637 |
Appl.
No.: |
06/947,164 |
Filed: |
December 29, 1986 |
Current U.S.
Class: |
244/130; 138/37;
138/39; 296/180.1; 296/180.4 |
Current CPC
Class: |
B62D
35/00 (20130101); B64C 23/00 (20130101); F42B
10/22 (20130101) |
Current International
Class: |
B62D
35/00 (20060101); B64C 23/00 (20060101); F42B
10/22 (20060101); F42B 10/00 (20060101); B64C
001/38 () |
Field of
Search: |
;244/130,200 ;296/1S
;105/1.1,1.2 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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452986 |
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Nov 1948 |
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CA |
|
822352 |
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Nov 1951 |
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DE |
|
845900 |
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Aug 1952 |
|
DE |
|
794841 |
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Feb 1936 |
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FR |
|
454600 |
|
Jan 1950 |
|
IT |
|
791563 |
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Mar 1955 |
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GB |
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Other References
"Axisymmetric Bluff Body Drag Reduction Through Geometrical
Modification", by Howard and Doodman, Journal of Aircraft, vol. 22,
#6, 6/85. .
"Longitudinal Grooves for Bluff Body Drag Reduction", by Howard,
Quass, Weinstein and Bushnell, AIAA Technical Note 81-4095, vol.
19, No. 4, Apr. 1981..
|
Primary Examiner: Barefoot; Galen
Assistant Examiner: Corl; Rodney
Attorney, Agent or Firm: Revis; Stephen E.
Claims
We claim:
1. An article adapted to be disposed in a fluid moving downstream
relative thereto, said article having a first surface extending
generally downstream, and a blunt end surface immediately
downstream of an adjoining said first surface and facing generally
downstream, a plurality of adjacent troughs formed in said first
surface extending in an axial direction, which is the direction of
the streamlines of the bulk fluid flow adjacent said surface in
which said troughs are disposed, and continuing to said end surface
to form a plurality of adjacent trough outlets in said end surface,
each of said troughs including a pair of downstream extending
sidewall surfaces which intersect said end surface to form side
edges of said trough outlets, wherein a portion of the area of said
blunt end surface extends laterally from each of said side edges of
each of said plurality of trough outlets to the side edge of an
adjacent trough outlet over the full length of each of said side
edges, wherein said laterally extending area portion between each
pair of adjacent trough outlets is at least one-fourth (1/4) of the
downstream projected area of one of said adjacent trough outlets,
wherein, in cross-section perpendicular to the downstream
direction, lines tangent to each sidewall of said pair of trough
sidewalls at their steepest point at said trough outlet are
substantially parallel, wherein each of said troughs has an inlet
and gradually increases from no depth at said inlet to its maximum
depth, and wherein the contour and dimensions of said troughs and
the size of said laterally extending area portions of said blunt
end surface are such as to ensure that each trough flows full
throughout its length and causes fluid to flow into the space
immediately downstream of said blunt end surface to reduce base
drag.
2. The article according to claim 1 wherein said pair of sidewall
surfaces of each trough are substantially parallel to the direction
of bulk fluid flow over said first surface in the vicinity of said
trough over a substantial continuous portion of the length of said
trough, said continuous portion including said trough outlet.
3. The article according to claim 1 wherein each of said troughs is
smoothly U-shaped along its length in cross section perpendicular
to the downstream direction.
4. The article according to claim 3 wherein said plurality of
troughs define a smoothly undulating surface which is wave-shaped
in cross section perpendicular to the downstream direction.
5. The article according to claim 1 wherein the sum of said
downstream projected areas of said trough outlets is no greater
than about 30% of the downstream projected area of said blunt end
surface.
6. The article according to claim 1 wherein each trough generates a
single large-scale axial vortex from each sidewall surface, said
pair of vortices from each trough rotating in opposite
directions.
7. The article according to claim 1 wherein said article has a
second surface extending generally downstream, and which is spaced
from and faces in a substantially opposite direction and away from
said first surface, said blunt end surface being disposed
immediately downstream of and adjoining said second surface, a
plurality of said troughs being formed in said second surface,
wherein a portion of the area of said blunt end surface extends
laterally from each of said side edges of said troughs in said
second surface to the side edge of an adjacent trough over the full
length of each of said side edges.
8. An article adapted to be disposed in a fluid moving downstream
relative thereto, said article having a first surface extending
generally downstream, and a blunt end surface immediately
downstream of and adjoining said first surface and facing generally
downstream, a plurality of adjacent troughs formed in said first
surface extending in an axial direction, which is the direction of
the streamlines of the bulk fluid flow adjacent said surface in
which said troughs are disposed, and continuing to said end surface
to form a plurality of adjacent trough outlets in said end surface,
the sum of the downstream projected areas of said troughs outlets
being no greater than about 30% of the downstream projected area of
said blunt end surface, each of said troughs including a pair of
downstream extending sidewall surfaces which intersect said end
surface to form side edges of said trough outlets, wherein a
portion of the area of said blunt end surface extends laterally
from each of said side edges of each of said plurality of trough
outlets to the side edge of an adjacent trough outlet over the full
length of each of said side edges, wherein each of said troughs has
an inlet and gradually increases from no depth at said inlet to its
maximum depth, wherein the contour and dimensions of said troughs
and the size of said laterally extending area portions of said
blunt end surface are such as to ensure that each trough flows full
throughout its length and causes fluid to flow into the space
immediately downstream of said blunt end surface to reduce base
drag.
9. The article according to claim 8 wherein said article has a
second surface extending generally downstream, and which is spaced
from and faces a substantially opposite direction and away from
said first surface, said blunt end surface being disposed
immediately downstream of and adjoining said second surface, a
plurality of said troughs being formed in said second surface,
wherein a portion of the area of said blunt end surface extends
laterally from each of said side edges of said troughs in said
second surface to the side edge of an adjacent trough over the full
length of each of said side edges.
10. The article according to claim 8 wherein the portion of the
downstream projected area of the blunt end surface disposed
laterally between each pair of adjacent trough outlets in each of
said first and second surfaces is at least one-fourth (1/4) of the
downstream projected area of one of said pair of trough
outlets.
11. The article according to claim 8 wherein said pair of sidewall
surfaces of each trough are substantially parallel to the direction
of bulk fluid flow over the surface in which said trough is
disposed over a substantial continuous portion of the length of
said trough, said continuous portion including said trough
outlet.
12. The article according to claim 8 wherein each of said troughs
is smoothly U-shaped along its length in cross section
perpendicular to the downstream direction.
13. The article according to claim 12 wherein each of said
plurality of troughs in each of said first and second surfaces
define a smoothly undulating surface which is wave-shaped in cross
section perpendicular to the downstream direction.
14. The article according to claim 8 wherein the blunt end surface
is a substantially flat surface perpendicular to the downstream
direction.
15. The article according to claim 8 wherein the article is a
vehicle and the blunt end surface is a rear end surface of said
vehicle.
16. A vehicle adapted to be disposed in a fluid moving downstream
relative thereto, said vehicle having a blunt rear end surface and
a first surface defining a first plurality of adjacent, downstream
extending troughs, each of said troughs terminating at said rear
end surface to form a plurality of spaced apart trough outlets in
said end surface, each of said troughs including a pair of
downstream extending sidewall surfaces which intersect said rear
end surface to form side edges of said trough outlets, wherein in
cross-section perpendicular to the downstream direction, lines
tangent to each sidewall of each of said pair of trough sidewalls
at their steepest point at said trough outlet are substantially
parallel, wherein a first portion of the area of said rear end
surface extends laterally from each of said side edges to the side
edge of an adjacent trough outlet over the full length of each of
said side edges, wherein the downstream projected area of the rear
end surface disposed laterally between each pair of adjacent trough
outlets of said first plurality of troughs is at least one-fourth
(1/4) of the downstream projected area of one of said pair of
adjacent trough outlets, wherein each of said troughs has an inlet
and gradually increases from no depth at said inlet to its maximum
depth, wherein the contour and dimensions of said troughs and the
size of said first area portions are such as to ensure that each
trough flows full throughout its length and causes fluid to flow
into the space immediately downstream of said rear end surface to
reduce base drag.
17. The vehicle according to claim 16 wherein said pair of sidewall
surfaces of each trough of said first plurality of troughs are
substantially parallel to the direction of bulk fluid flow over
said first surface in the vicinity of said trough over a
substantial continuous portion of the length of said trough, said
continuous portion including said trough outlet.
18. The vehicle according to claim 16 wherein each of said troughs
of said first plurality of troughs is smoothly U-shaped along its
length in cross section perpendicular to the downstream
direction.
19. The vehicle according to claim 18 wherein said first plurality
of troughs define a smoothly undulating surface which is
wave-shaped in cross section perpendicular to the downstream
direction.
20. The vehicle according to claim 16 wherein the sum of said
downstream projected areas of all of said trough outlets is no
greater than about 30% of the downstream projected area of said
rear end surface.
21. The vehicle according to claim 16 wherein said vehicle has a
second surface spaced from and facing in a direction substantially
opposite to and away from said first surface and defining a second
plurality of said downstream extending troughs.
22. The vehicle according to claim 21 wherein the portion of the
downstream projected area of said rear end surface disposed
laterally between each pair of adjacent trough outlets of said
second plurality of troughs is at least one-fourth (1/4) of the
downstream projected area of one of said pair of trough
outlets.
23. The vehicle according to claim 22 wherein each of said first
and second plurality of troughs defines a smoothly undulating
surface which is wave-shaped in cross section perpendicular to the
downstream direction.
24. The vehicle according to claim 21 wherein each of said troughs
of said first and second plurality of troughs is smoothly U-shaped
along its length in cross section perpendicular to the downstream
direction.
25. The vehicle according to claim 21 wherein the sum of said
downstream projected areas of all of said trough outlets is no
greater than about 30% of the downstream projected area of said
rear end surface.
26. The vehicle according to claim 21 wherein said pair of sidewall
surfaces of each trough are substantially parallel to the direction
of bulk fluid flow over the surface in which said trough is
disposed over a substantial continuous portion of the length of
said trough, said continuous portion including said trough
outlet.
27. The vehicle according to claim 16 wherein said rear end surface
is a substantially flat surface perpendicular to the downstream
direction.
28. The vehicle according to claim 16 wherein each trough generates
a single large-scale vortex from each sidewall surface, each of
said vortices having and axis extending downstream, said pair of
vortices from each trough rotating in opposite directions.
29. A vehicle adapted to be disposed in a fluid moving downstream
relative thereto, said vehicle having a blunt rear end surface and
a first surface defining a first plurality of adjacent, downstream
extending troughs, each of said troughs terminating at said rear
end surface to form a plurality of spaced apart trough outlets in
said end surface, the sum of the downstream projected areas of all
of said trough outlets being no greater than about 30% of the
downstream projected area of said rear end surface, each of said
troughs including a pair of downstream extending sidewall surfaces
which intersect said rear end surfaces to form side edges of said
trough outlets, wherein a first portion of the area of said rear
end surface extends laterally from each of said side edges to the
side edge of an adjacent trough outlet over the full length of each
of said side edges, wherein each of said troughs has an inlet and
gradually increases from no depth at said inlet to its maximum
depth, wherein the contour and dimensions of said troughs and the
size of said first area portions are such as to ensure that each
trough flows full throughout its length and causes fluid to flow
into the space immediately downstream of said rear end surface to
reduce base drag.
30. The vehicle according to claim 29 wherein said pair of sidewall
surfaces of each trough of said first plurality of troughs are
substantially parallel to the direction of bulk fluid flow over
said first surface in the vicinity of said trough over a
substantial continuous portion of the length of said trough, said
continuous portion including said trough outlet.
31. The vehicle according to claim 29 wherein each of said troughs
of said first plurality of troughs is smoothly U-shaped along its
length in cross section perpendicular to the downstream
direction.
32. The vehicle according to claim 31 wherein said first plurality
of troughs define a smoothly undulating surface which is
wave-shaped in cross section perpendicular to the downstream
direction.
33. The vehicle according to claim 29 wherein said vehicle has a
second surface spaced from and facing in a direction substantially
opposite to and away from said first surface and defining a second
plurality of said downstream extending troughs.
34. The vehicle according to claim 33 wherein each of said first
and second plurality of troughs defines a smoothly undulating
surface which is wave-shaped in cross section perpendicular to the
downstream direction.
35. The vehicle according to claim 33 wherein each of said troughs
of said first and second plurality of troughs is smoothly U-shaped
along its length in cross section perpendicular to the downstream
direction.
36. The vehicle according to claim 33 wherein said pair of sidewall
surfaces of each trough are substantially parallel to the direction
of bulk fluid flow over the surface in which said trough is
disposed over a substantial continuous portion of the length of
said trough, said continuous portion including said trough
outlet.
37. The vehicle according to claim 29 wherein said rear end surface
is a substantially flat surface perpendicular to the downstream
direction.
38. The vehicle according to claim 29 wherein each trough generates
a single large-scale vortex from each sidewall surface, each of
said vortices having an axis extending downstream, said pair of
vortices from each trough rotating in opposite directions.
Description
TECHNICAL FIELD
The present invention relates to reducing base drag.
BACKGROUND ART
Drag is the result of skin friction and surface pressure variations
induced by viscous effects, especially those due to separation
bubbles or regions (i.e., low pressure wakes). Separation regions
occur when two and three dimensional boundary layers depart from
the surface of the body. Bluff or blunt bodies have shapes which
tend to promote a rapidly increasing downstream pressure gradient
in the streamline flow around it which can cause the bulk flow to
break loose from the surface of the body. This is particularly true
for bodies having blunt end surfaces, such as automobiles, tractor
trailors, and blunt ended projectiles. The separation bubbles
created behind these objects as they move through the air produce
high base drag.
Airfoil shaped bodies such as airplane wings, rudders, sails, and
gas turbine engine rotor blades and stator vanes have a streamlined
shape which, at moderate angles of attack (below about 15.degree.)
avoid streamwise two-dimensional boundary layer separation over the
entire surface. At higher angles of attack (or increased loading)
separation does occur and a recirculating flow region (or a low
pressure wake) is formed, greatly increasing drag and reducing
lift. As used in the specification and appended claims,
"streamwise, two-dimensional boundary layer separation" means the
breaking loose of the bulk fluid from the surface of a body,
resulting in a flow near the wall moving in a direction opposite
the bulk fluid flow direction.
It has been a constant goal of aerodynamicists to reduce the drag
and improve lift and stall characteristics (if appropriate) on
bodies disposed in a fluid moving relative thereto. A common way to
avoid boundary layer separation on an airfoil (or other streamlined
body) or to at least delay separation such that it occurs as far
downstream along the surface of the airfoil as possible so as to
minimize drag, is to reduce the pressure rise downstream such as by
tailoring the surface contour along the length of the airfoil in
the direction of bulk fluid flow.
Another well known method for reducing the drag on airfoils is to
create turbulence in the boundary layer so as to impart a greater
average momentum of the boundary layer fluid, which carries it
further downstream along the surface against an adverse pressure
gradient, thereby delaying the separation point. For example, U.S.
Pat. No. 4,455,045 to Wheeler describes elongated, expanding
channels in the flow surface. The channels have sharp, lengthwise
edges. The boundary layer on the surface flows into the channels,
and the channel edges create streamwise vortices below the level of
the normal flow surface which energize the flow in the channel to
maintain boundary layer attachment of the flow along the floor of
the channel.
Similarly, Stephens creates a plurality of adjacent streamwise
extending channels in the flow surface. The channels continuously
expand laterally from a narrow inlet to a wide outlet. A generally
triangular ramp is formed between adjacent channels. Stephens
explains that the boundary layer flow is split between the ramps
and the channels. The flow within the channels spreads out and the
boundary layer becomes thinner and remains attached to the surface
longer. The ramp flow is diverted into the general flow. One
application (FIG. 6 of Stephens) is between the roof and rear
window of an automobile to maintain the flow attached to the curved
surface for a greater distance than normal.
In U.S. Pat. No. 1,773,280 to Scott, increased lift without
increased drag is created for an aircraft wing by placing a
plurality of side-by-side chordwise extending ridges along the top
of the wing from its leading to its trailing edge, the ridges
having their highest point near the thickest portion of the wing.
The ridges themselves are airfoil shaped when viewed from above,
tapering to a point at the trailing edge of the wing. This concept
does not take into account viscous induced boundary layer
separation effects and therefore could not be expected to avoid
separation at high lift conditions.
U.S. Pat. No. 3,588,005 to Rethorst uses chordwise extending ridges
in the upper surface of an airfoil to delay the onset of separation
by providing "channels of accelerated flow in the free stream flow
direction to add energy to the boundary layer and maintain laminar
flow in the region of normally adverse pressure gradient". The
ridges protrude from the surface "to a height of the order of the
boundary layer thickness". Cross flow components "are accelerated
over the ridges and may reduce the likelihood of separation near
the aft end . . . of the body by allowing the flow to `corkscrew`
smoothly off the aft end rather than encounter the abrupt adverse
pressure gradient in the free stream direction caused by a blunted
aft end". As with the ridges of the Scott patent discussed above,
flow is also accelerated between the ridges which further helps
maintain laminar flow over the airfoil surface.
U.S. Pat. Nos. 3,741,235 and 3,578,264 to Kuethe delay separation
by creating vortices using a series of crests or concave
depressions which extend substantially transverse to the streamwise
flow direction. Kuethe states that the maximum height of a crest or
depth of a depression is preferably less than the boundary layer
thickness.
In a paper titled "The Reduction of Drag by Corrugating Trailing
Edges" by D. L. Whithead, M. Kodz, and P. M. Hield published by
Cambridge University, England in 1982, blunt case drag of a blade
(having a 20-inch span, 20-inch chord length, a constant thickness
of 1.5 inches and a blunt trailing edge) is reduced by forming the
last seven inches of its chordwise length into streamwise
extending, alternating troughs and ridges (corrugations). The
trailing edge and any upstream cross-section across the
corrugations has the shape of a sine wave with an 8.0 inch
wavelength. The thickness of the blade material is maintained
constant over the length of each trough and ridge, although the
trough depth or ridge height (i.e., wave amplitude) transitions
from a maximum of 2.0 inches at the trailing edge to zero upstream.
The total trough outlet area is more than 50% of the blunt base
area. FIGS. 21-23 show the blade described therein, with dimensions
given in terms of a unit length "a". A reduction of base drag of
about one-third was realized when compared with a reference blade
without corrugation. It is explained that spanwise vortices which
were shed alternately from the top and bottom rear edges of the
non-corrugated reference blade were eliminated by the
corrugations.
In general, it is believed that the separation delaying devices of
the prior art create significant drag in their own right, thereby
negating some of the benefits they would otherwise provide. This
sometimes limits their effectiveness. While many of the devices of
the prior art have proved to be effective in reducing drag, further
improvement is still desired, such as with respect to reducing base
drag on blunt based objects.
DISCLOSURE OF THE INVENTION
One object ofthe present invention is to reduce the drag on blunt
ended bodies.
Another object of the present invention is to reduce the size of
the separation bubble downstream of a blunt ended body.
According to the present invention, an article adapted to be
disposed in a fluid stream moving downstream relative thereto has a
generally streamwise extending surface which terminates as a blunt,
generally downstream facing end surface, wherein a plurality of
troughs are disposed in the streamwise extending surface and extend
to the blunt end surface in the direction of the near bulk fluid
flow forming trough outlets in the end surface, the troughs being
constructed and designed to flow full and to cause the fluid
flowing therefrom to move into the space immediately behind the
blunt end surface to reduce size of the separation bubble which
would otherwise be formed. In other words, the present invention
reduces the intensity of the low pressure wake formed immediately
behind a blunt end surface.
In this application the blunt end surface of an article may be
either a downstream facing end surface formed by a rapidly
increasing rate of curvature of a generally streamwise extending
surface, or the downstream facing end surface at which a streamwise
extending surface terminates abruptly, such as when the end surface
is essentially perpendicular to the streamwise surface. The troughs
of the present invention must be contoured and sloped such that
they flow full (i.e., no streamwise, two-dimensional boundary layer
separation occurs within the troughs). Thus, the troughs must
extend from a point upstream of where boundary layer separation
would normally occur. The troughs are preferably U-shaped in cross
section taken perpendicular to the downstream direction and are
preferably smoothly curved (i.e., no sharp angles where trough
sidewall surfaces meet the trough floor) to minimize losses. Most
preferably the troughs form a smoothly undulating surface which is
wave-shaped in cross section perpendicular to the downstream
direction.
Commonly owned U.S. patent application Ser. No. 857,907 filed on
Apr. 30, 1986 titled Airfoil Shaped Body, by Walter M. Presz, Jr.
et al (hereinafter the '907 application) describes an airfoil
trailing edge region with streamwise troughs and ridges formed
therein defining a wave-like, thin trailing edge. The troughs in
one surface define the ridges in the opposing surface. The troughs
and the ridges help delay or prevent the catastrophic effects of
two-dimensional boundary layer separation on the airfoil suction
surface, by providing three-dimensional relief for the low momentum
boundary layer flow. The present invention, however, is directed to
reducing the base drag created behind a blunt based article. One
distinction between the '907 application and the present invention
is that in the present invention the troughs need only be formed in
one surface. Additionally, the troughs can have a significant
effect even when the blunt end surface area is much greater than
the sum of the trough outlet areas, even twenty times greater or
more.
It is believed that the fluid leaves the troughs with a direction
of momentum that carries it over the blunt end surface into the
normally stagnant region behind the blunt end surface (i.e., a
downwash is created). Additionally, it is believed that each trough
generates a single, large-scale axial vortex from each side wall
surface at the trough outlet. (By "large-scale" it is meant the
vortices have a diameter about the size of the overall trough
depth.) These two vortices rotate in opposite directions and create
a flow field which tends to cause fluid from the trough and also
from the nearby bulk fluid to move into the region behind the blunt
surface. The net effect of this phenomenon either alone or coupled
with the downwash effect, is to reduce the size of the stagnation
bubble normally formed behind a blunt end surface, thereby reducing
base drag. Additionally, in cases where the shedding of spanwise
vortices is an additional contributor to base drag, it is believed
that the troughs suppress such shedding.
Adjacent troughs should be spaced far enough apart such that the
counter-rotating axial vortices tending to be generated from the
sidewall surfaces of adjacent troughs have enough space to become
fully developed. If the troughs are too close together the
counter-rotating vortices will interfere with each other or cancel
each other out.
According to another aspect of the present invention, it is
preferred that the fluid exit from each trough with the least
possible lateral component of velocity to minimize secondary flow
losses. For this reason the trough sidewalls, for a significant
distance upstream of the outlet, are preferably parallel to the
direction of bulk fluid flow adjacent the surface in the vicinity
of the trough.
In accordance with another aspect of the present invention, it is
preferred that the trough sidewalls at the outlet be steep, most
preferably substantially perpendicular to the streamwise extending
surface. This is believed to increase the intensity of the vortex
generated by the sidewall. The word "steep" as used herein and in
the claims means that, in cross section perpendicular to the
direction of trough length, lines tangent to the steepest point on
each sidewall intersect to form an included angle of no more than
about 120.degree..
The present invention is particularly suitable for use on bodies
having oppositely facing, downstream or streamwise extending
surfaces which are joined by a blunt, downstream facing end surface
substantially perpendicular to the flow direction. In that instance
a plurality of downstream extending troughs may be formed in both
oppositely facing surfaces, with the trough outlets in the blunt
end surface. Whether or not troughs are formed in one or both
surfaces, the troughs should have a depth at their outlets and be
of sufficient cross-sectional flow area relative to the total
surface area of the blunt end surface to have a not insignificant
effect on the separation bubble which would normally be formed. A
minimum trough outlet depth of only a few percent of the distance
between the oppositely facing surfaces at the trough outlets can be
effective. The troughs in each surface may have a corresponding
trough directly opposite it in the other surface (i.e., a
symmetrical trough outlet pattern); or, the trough outlets may be
staggered, alternating from side to side along the transverse
length of the end surface (i.e., a non-symmetrical trough outlet
pattern). The troughs in opposing surfaces each create a flow of
fluid across the blunt end surface toward the opposite side. If the
opposite surfaces are close enough to each other for the flows from
the troughs to interact, the non-symmetrical pattern is believed to
be preferred since the alternating regions of upwash and downwash
may reinforce each other.
The foregoing and other objects, features and advantages of the
present invention will become more apparent in the light of the
following detailed description of preferred embodiments thereof as
illustrated in the accompanying drawing.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates the fluid dynamics associated with a blunt based
body moving relative to a fluid stream.
FIG. 2 is a perspective view of a blunt based article incorporating
the features of the present invention.
FIG. 3 is a sectional view taken along the line 3--3 of FIG. 2.
FIG. 4 is a view taken generally in the direction of the line 4--4
of FIG. 3.
FIG. 5 is a sectional view taken generally in the direction of the
line 5--5 of FIG. 4.
FIG. 6 is an enlarged view of the area designated Y in FIG. 4.
FIG. 7 is a perspective view of an automobile which incorporates
the present invention.
FIG. 8 is an end view of the automobile taken generally in the
direction of the line 8--8 of FIG. 7.
FIG. 9 is a partial sectional view taken along the line 9--9 of
FIG. 8.
FIG. 10 is a side elevation view of a tractor trailer which
incorporates the present invention.
FIG. 11 is an end view of the tractor trailer taken generally in
the direction of the line 11--11 of FIG. 10.
FIG. 12 is a partial perspective view of a blunt ended body which
incorporates another embodiment of the present invention.
FIG. 13 is a sectional view taken along the line 13--13 of FIG.
12.
FIG. 14 is an end view taken in the direction of the line 14--14 of
FIG. 13.
FIG. 15 is a side elevation view of a projectile incorporating the
present invention.
FIG. 16 is an end view of the projectile of FIG. 15 taken generally
in the direction of the line 16--16 of FIG. 15.
FIG. 17 is a partial perspective view of an airfoil which
incorporates the present invention in its trailing edge.
FIG. 18 is a view taken generally in the direction 18--18 of FIG.
17.
FIG. 19 is a view taken generally in the direction of the line
19--19 of FIG. 18.
FIG. 20 is an illustrative perspective view of an airfoil showing
an alternate embodiment of the present invention.
FIG. 21 is a perspective view of a "blade" in accordance with the
prior art.
FIG. 22 is a cross sectional view taken along the line 22--22 of
prior art FIG. 21.
FIG. 23 is a cross sectional view taken along the line 23--23 of
prior art FIG. 21.
BEST MODE FOR CARRYING OUT THE INVENTION
FIG. 1 illustrates what occurs when fluid flows over the surface of
a body which terminates at a blunt downstream end. In this figure
the body is represented by the reference numeral 10, and includes
upper and lower smooth, flat surfaces 12, 14, respectively, over
which fluid is flowing. The wide arrows 16 represent the downstream
direction, while the lines 18 represent streamlines of the bulk
fluid flowing adjacent the surfaces 12, 14. As is well known in the
art, although the fluid may stay attached to the smooth surfaces
12, 14 under a wide range of conditions, it cannot turn the corner
when it reaches the blunt end surface 20, resulting in separation
at or near the upper and lower edges 22, 24. The flow off the upper
and lower surfaces rejoin each other at some point downstream of
the surface 20. Upstream of that point there is a low pressure
region 21 (or "separation bubble") between the upper and lower
streamlines immediately downstream of the blunt end surface 20. If
the fluid flow is the result of the body 10 moving through the
fluid in an upstream direction, this low pressure stagnation region
results in a force in the downstream direction which resists or is
opposite to any force attempting to move the body in the upstream
direction. This force is referred to as the base drag, and can be
substantial.
The present invention reduces base drag while introducing minimal
other losses which counteract the benefits of reduced base drag.
The invention is illustratively shown and described with reference
to FIGS. 2-6. As shown in FIG. 2, an article incorporating the
present invention is generally represented by the numeral 30. The
article has an upper surface 32 and a lower surface 34. It is
assumed that the article is moving through a fluid, such as air, in
an upstream direction generally represented by the arrow 36. The
downstream direction is represented by the arrow 38. According to
the present invention a plurality of downstream extending troughs
40 are formed in the upper surface 32; and a plurality of
downstream extending troughs 42 are formed in the lower surface 34.
The troughs are generally U-shaped in cross section taken
perpendicular to the downstream direction. Each trough extends from
its respective inlet 43 to a blunt end surface 44 which joins the
upper and lower surfaces 32, 34 and faces substantially
downstream.
The troughs must be contoured, sized and shaped to flow full over
their entire length such that streamwise boundary layer separation
does not occur within the troughs. In this regard, the fluid
flowing along the surfaces 32, 34 must be attached to such surfaces
(i.e., no streamwise boundary layer separation) as it enters the
trough inlets. The trough outlets 45 in the end surface 44 have an
amplitude or depth A (FIG. 6). They have zero depth at their
upstream ends and blend smoothly into their respective upper and
lower surfaces at their upstream ends and along their length. In
this preferred embodiment each trough increases in depth from its
upstream end to its outlet. However, this is not required. For
example, the depth could reach a maximum upstream of the trough
outlet and then remain constant to the outlet.
In this exemplary embodiment the troughs are smoothly U-shaped
along their length in cross section perpendicular to the downstream
direction and define a smoothly undulating surface which is wave
shaped in cross section perpendicular to the downstream direction.
Each trough has a pair of facing sidewall surfaces 46 which
terminate as side edges 48 of the trough outlet 45. Preferably the
sidewall surfaces 46 are substantially parallel to the direction of
bulk fluid flow over the surface in which they are disposed over a
substantial continuous portion of the length of the trough, which
includes the trough outlet. The parallel nature of the sidewall
surfaces 48 is best shown in FIG. 5. It is undesirable that the
sidewalls diverge since it contributes to streamwise separation
within the troughs and introduces lateral velocity components in
the fluid leaving the trough, which create undesirable secondary
flow losses.
It is believed that a couple of different fluid dynamic mechanisms
are responsible for the reduced base drag resulting from the
present invention, although these mechanisms are not fully
understood. It is felt, for example, that there is a bulk motion of
the fluid leaving the troughs which motion is into the space
immediately behind and adjacent the blunt end surface as if it
were, to some extent, remaining attached to the blunt end surface
of the article after it exits the troughs. Second, it is believed
that each trough generates a pair of large-scale axial vortices,
the axial direction being the downstream direction. Each vortex is
generated off of a respective one of the two trough side edges 48.
The vortices of each pair rotate in opposite directions. These
vortices create a flow field which tends to cause fluid from the
trough and from the nearby bulk fluid to move into the region
behind and adjacent the blunt surface.
In order that the vortex generated off of the side edge 48 of one
outlet is not interfered with (i.e., cancelled out) by a
counterrotating vortex generated off the side edge of the next
adjacent trough it is necessary that the side edges of adjacent
troughs be spaced apart by a sufficient distance. Thus, it is
necessary that a portion of the area of the blunt end surface 44
extend laterally from the side edge 48 of each trough outlet to the
side edge 48 of an adjacent trough outlet over the full length of
each of the side edges. This area of the blunt end surface is
represented by the cross hatched area 50 of FIG. 6 disposed between
the trough side edges designated by the reference numerals 48A and
48B. In general, the downstream projection of the area 50 between
the side edges of adjacent troughs should be at least about
one-fourth (1/4) of the downstream projected outlet area of a
trough.
It is further believed that best results are obtained when the side
wall surfaces 48 at the outlet are steep. Preferably, in a cross
section perpendicular to the downstream direction, which is the
direction of trough length, lines 52 tangent to the steepest points
along the side edges 48 should form an included angle C (FIG. 6) of
no greater than about 120.degree.. The closer angle C is to zero
degrees (0.degree.), the better.
The troughs should be large enough in downstream projected
cross-sectional area at their outlets, relative to the total
downstream projected area of the blunt end surface to have a
worthwhile impact on the base drag. For some applications a total
trough outlet area which is only a few percent of the total blunt
base area may produce a measureable reduction in base drag. For
most applications a trough outlet area no more than 30% of the
total blunt base area would be used due to practical
considerations.
It is also believed that the troughs should not be too narrow
relative to their depth, otherwise appropriate flow patterns within
the trough will not develop and the desired base drag reduction
will not occur. With reference to FIG. 6, the trough width at its
outlet is considered to be the peak to peak wave length P, and the
trough depth at the outlet is considered to be the peak to peak
wave amplitude A. The ratio P/A should be greater than about 0.25
and preferably at least 0.5. Additionally, the ratio P/A should be
less than about 4.0.
The results will also not be very effective if the trough is too
long relative to its outlet depth (amplitude) since the appropriate
flow fields generated within the trough will dampen out before
reaching the outlet. It is believed that the ratio of trough length
to outlet amplitude should be no greater than about 12 to 1.0.
Although in the embodiment of FIGS. 2-6 the end surface 44 is flat
and perpendicular to the downstream direction, the invention may be
applied to blunt ends of other shapes (see FIGS. 12-14).
In FIGS. 7-9 a trough configuration similar to that shown in FIGS.
2-6 is incorporated in the rear end of an automobile generally
represented by the reference numeral 100. The troughs 101 are
formed in the upper trunk surface 102 and in the under surface 104
of the vehicle. The troughs intersect the rearwardly facing blunt
end surface 106. One distinction between the embodiment of FIGS.
7-9 and the embodiment of FIGS. 2-6 is that the troughs 101 are
formed by adding lobes 110 to the original vehicle contours
represented by the lines 112 and 114.
As a test, a 1/25th scale model of a Pontiac Firebird Trans-Am was
purchased and troughs were formed on the trunk lid surface and on
the under surface of the car by adding material as opposed to
cutting away material. This resulted in adding additional blunt
base area to the automobile. The floor or bottom of each trough
followed approximately the contour of the original surface of the
vehicle. Referring to FIGS. 8 and 9, the overall dimensions of the
blunt end surface were H=1.4 inches and W=2.9 inches. The length L
of the troughs was 1.4 inches. The troughs formed a smoothly
undulating surface which was wave shaped in cross section taken
perpendicular to the downstream direction. The wave had a period of
0.6 inches and a peak to peak amplitude of 0.3 inches. The angle
corresponding to the angle C of FIG. 6 was 90.degree.. The surfaces
112, 114 each formed an angle of only about 12.degree. with a
horizontal plane.
In a wind tunnel test at a velocity of 75 ft/sec the modified model
incorporating the present invention had an overall drag 16 percent
less than the overall drag on the model prior to modification,
despite an approximately 12.5 percent increase in the base surface
area. Since only the rear end of the vehicle was modified, it can
be assumed that the overall drag reduction was essentially due to
reduced base drag.
FIGS. 10 and 11 show the present invention applied to a trailer
truck generally designated by the reference numeral 150. As shown,
troughs 152 are formed as depressions in the normally flat side
surfaces and the top and bottom surfaces of the trailer. The trough
outlets 154 are in the plane of the blunt rear end surface 156 and
form a smooth wave shape along the four edges of the end surface
156. Although formed as depressions, the troughs could equally well
have been formed by adding material to the trailer surfaces as was
done to the automobile 100 shown in FIGS. 7-9.
Another embodiment of the present invention is illustrated in FIGS.
12-14. Note that there are troughs 200 only in one surface. Also,
the troughs 200 are semicircular in cross section at all points
along their length and form relatively sharp edges 202 with the
smooth, flat surface 204 in which they are disposed. Although sharp
edges are not preferred since they induce losses, it is believed
that a significant net benefit may stil be obtained with such a
configuration. As best seen in FIG. 13, the bottom surface 206 of
each trough blends smoothly with the surface 204 at the upstream
end 205 of the trough and has its outlet 210 in the curved blunt
end surface 209. The outlets 210 are located upstream of where
boundary layer separation from the surface 204 would normally occur
(i.e., without troughs). As discussed with respect to the
embodiment of FIGS. 2-6, the downstream projection of the blunt
surface area portion 211 (shaded) disposed laterally between each
pair of adjacent troughs should have an area which is at least one
quarter (1/4) of the downstream projected area of a trough
outlet.
The trough configuration of the present invention may also be used
to reduce the base drag of a projectile, such as the ballistic
shell 300 shown in FIGS. 15 and 16. Projectiles of this type
typically rotate in flight about their longitudinal axis, such as
the axis 302 of the shell 300, for purposes of aerodynamic
stability. The direction of rotation is represented by the arrow R.
The shell 300 has an axial velocity V represented by the vector
V.sub.1. The vector V.sub.2, which is tangent to the shell surface
306, represents the rotational velocity of the shell external
surface 306 at the shell downstream end 304. Each trough extends
generally parallel to the direction of the sum of the vectors
V.sub.1 and V.sub.2. This trough orientation is required in order
that the fluid flows into the troughs in a direction substantially
parallel to the trough length.
Although troughs of generally semicircular cross section (like
those described with respect to FIGS. 12-14) are shown in this
embodiment, the troughs could also be configured as shown in the
embodiment of FIGS. 4-6 (i.e., U-shaped troughs formed by a
smoothly undulating surface, wave-shaped in cross section
perpendicular to the downstream direction).
The present invention may also be applied to the thin trailing edge
of an airfoil, such as the gas turbine engine compressor rotor
blade shown in FIGS. 17-19. The airfoil is generally represented by
the reference numeral 400. The direction of the engine axis is
represented by the arrow 401 in FIG. 19, which is the downstream
direction. The airfoil 400 has a pressure surface 402 and a suction
surface 404 which converge toward each other to form a thin
trailing edge 406. Although an airfoil thin trailing edge is not
normally considered to be "blunt", it is believed that fluid
boundary layers which remain attached to the pressure and suction
surfaces even down to the very end of the airfoil ultimately
separate from the trailing edge 406 in a manner which creates a
narrow, but not negligible, separation region immediately
downstream of and adjacent the trailing edge. Therefore, for
purposes of this embodiment, the end surface 407 is considered to
be a blunt end surface.
In this embodiment the troughs of the present invention are shown
cut into (i.e., formed) in both the suction surface 404 (troughs
408) and the pressure surface 402 (troughs 410); however, troughs
in only one of those surfacesis also contemplated as being within
the scope of the present invention. If there are troughs in both
the pressure and suction surfaces, the outlets of the troughs in
one surface are preferably laterally offset from the troughs in the
other surface (i.e. a non-symmetrical trough pattern). The depth of
the troughs at their outlet should not exceed about 50% of the
trailing edge thickness T.
Each trough extends in a direction approximately parallel to the
direction of the bulk fluid flow streamlines in its vicinity
adjacent the surface in which the trough is disposed. The object is
to have the troughs oriented such that fluid flows into each trough
essentially parallel to the direction of trough length. Due to
blade rotation, the local bulk fluid flow direction adjacent the
blade surface varies along the blade length. Thus the trough
orientation will vary along the blade length as does the radial
component of the fluid velocity. The selected orientation will
generally be based upon cruise conditions to maximize benefits.
In this embodiment the planes of both the pressure and suction
surfaces extend to the surface 407 between the edges 412 of
adjacent troughs. As explained with respect to other embodiments of
the present invention, the lateral distance D between adjacent
trough outlets in each surface should be selected to assure thatthe
downstream projected area of the blunt end surface 407 disposed
laterally between the outlet edges of adjacent troughs in each
surface is at least about one-fourth (1/4) of the outlet area of
one of the troughs. The other teachings concerning trough contour
and size taught in conjunction with the other embodiments of the
present invention are also applicable to this embodiment.
As shown in the alternate airfoil embodiment of FIG. 20, the
troughs 500 may also be formed by building up the airfoil pressure
and/or suction surfaces 502, 504, respectively, in the trailing
edge region 506. This actually increases the downstream projected
susrface area of the blunt trailing edge 508 such that it is even
greater than the area of a longitudinal cross section 510 taken
upstream of the trailing edge surface along the trough inlets, such
as in the plane 512 shown in phantom. The net base drag may be
reduced despite this increase in blunt base area.
Although the invention has been shown and described with respect to
a preferred embodiment thereof, it should be understood by those
skilled in the art that other various changes and omissions in the
form and detail of the invention may be made without departing from
the spirit and scope thereof.
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